Persistence of Invariant Manifolds for Perturbations of Semiflows with Symmetry
Southwest Texas State University, Department of Mathematics
Consider a semiflow in a Banach space, which is invariant under the action of a compact Lie group. Any equilibrium generates a manifold of equilibria under the action of the group. We prove that, if the manifold of equilibria is normally hyperbolic, an invariant manifold persists in the neighborhood under any small perturbation which may break the symmetry. The Liapunov-Perron approach of integral equations is used.
Semiflow, Invariant manifold, Symmetry
Zeng, C. (1999). Persistence of invariant manifolds for perturbations of semiflows with symmetry. <i>Electronic Journal of Differential Equations, 1999</i>(16), pp. 1-13.